To find the perimeters of the triangles and the ratio of the corresponding sides, we can follow these steps:
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Calculate the perimeter of the smaller triangle: The side lengths of the smaller triangle are 2, 6, and 7 units. The perimeter (P) is given by: \[ P_{\text{small}} = 2 + 6 + 7 = 15 \text{ units} \]
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Calculate the perimeter of the larger triangle: The side lengths of the larger triangle are 6, 18, and 21 units. The perimeter is: \[ P_{\text{large}} = 6 + 18 + 21 = 45 \text{ units} \]
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Calculate the ratio of the corresponding sides: To find the ratio of the sides of the smaller triangle to the corresponding sides of the larger triangle, we take one set of corresponding sides. For example:
- For side lengths 2 (smaller) and 6 (larger), the ratio is \( \frac{2}{6} = \frac{1}{3} \).
- For side lengths 6 (smaller) and 18 (larger), the ratio is \( \frac{6}{18} = \frac{1}{3} \).
- For side lengths 7 (smaller) and 21 (larger), the ratio is \( \frac{7}{21} = \frac{1}{3} \).
In each case, the ratio of corresponding sides of the smaller triangle to the larger triangle is \( \frac{1}{3} \).
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Conclusion:
- The perimeter of the smaller triangle is 15 units.
- The perimeter of the larger triangle is 45 units.
- The ratio of the corresponding sides of the smaller triangle to the larger triangle is \( \frac{1}{3} \).
Thus, the final results are:
- Perimeter of smaller triangle: 15 units
- Perimeter of larger triangle: 45 units
- Ratio of corresponding sides: \( \frac{1}{3} \)
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